On the Hausdorff Dimension of the Spectrum of the Thue–Morse Hamiltonian

2014/09/17 by Qinghui Liu, Yanhui Qu · 7 citations
Materials Science · Mathematics · Physics and Astronomy · #Effective dimension #Geometric and Algebraic Topology #Hamiltonian (control theory) #Hamiltonian system #Hausdorff dimension #Hausdorff distance #Hausdorff measure #Hausdorff space #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties #Spectrum (functional analysis) #Upper and lower bounds #math-ph #math.DS #math.MP #math.SP #msc:37C45 #msc:37E20 #msc:81Q10

paper · pdf · doi:10.1007/s00220-015-2377-x

published in Communications in Mathematical Physics 338(2), 867-891 (Springer Science+Business Media) · substantial overlap with arXiv:1403.2257

arxiv created 2014/09/17 · openalex publication_date 2015/05/06 · arxiv updated 2015/06/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show that the Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian has a common positive lower bound for all coupling.

Citations

• Iteration of polynomial pair under Thue-Morse dynamic
• The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
• Hyperbolicity of the trace map for the weakly coupled Fibonacci Hamiltonian
• Spectral and Quantum Dynamical Properties of the Weakly Coupled Fibonacci Hamiltonian